Grade: 7 Unit: 2 Week: 5 Dates: 10/29 – 11/2 Content: Solving Problems with Expressions, Equations, and Inequalities (w/o percentages)
Theme Essential Question:
How can you use numerical and algebraic expressions, equations, and inequalities to solve real-life mathematical problems?
Essential Questions:
How can you solve problems by using expressions, equations, and inequalities?
How do you solve equations and inequalities containing multiple operations?
How do use estimation strategies to assess reasonableness of solutions?
Standards:
7. EE.3 Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.
Objectives:
The student will use a bar model to solve problems.
The student will draw pictures and label them to help write equations to solve problems.
The student will write equations and inequalities to solve word problems.
The student will use estimation strategies in assessing reasonableness of solutions to problems.
Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team The percentage problems associated with expression, equations, and inequalities have been moved to Unit 3 on Ratios and Proprotions. The problems omitted in this unit will be re-introduced in lesson 3-5.
Background Information Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials at http://www.azed.gov/educator-certification/
Assessment: Product Problem solving using equations
Students will work with a partner to design a problem that uses a bar model.
They will solve for an appropimate solution.
They will find the actual solution and compare the two solutions.
They will prepare a display of their work.
OR Struggling Students
Students will work with a partner to design two problems similar to the ABC Mastering the Common Core in Mathematics Chapter 9.10, p. 111.
They will solve the problems
They will prepare a display that provides clarity to the solution.
A visual sketch depicting the word problem
Identify the variable
Detail the approached used to solve the problem
Key Questions
What is a bar model?
How do you use a bar model to help solve a problem?
How do you use variables in your drawing of a problem to help solve it?
How do you know when to use an equation or an inequality?
How do you know if you answer makes sense?
Observable Student Behaviors
The student can develop solutions, while provided written and/or verbal justifications, to support their approach to word problems (equations and inequality).
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Vocabulary:
Math
Bar model Inequalities Inequality signs Inverse operations Solution set Validate
Suggested Activities:
Houghton Mifflin On Core Mathematics Middle School Grade 7 Unit 3-6, p. 77-80
ABC Mastering the Common Core in Mathematics Chapter 9.10, p. 111
Teaching the Common Core Math Standards with Hands-On Activities
7.EE.3, Activity, Estimation Game, p. 108
Gizmo
Air Track
Adjust the mass and velocity of two gliders on a frictionless air track. Measure the velocity, momentum, and kinetic energy of each glider as they approach each other and collide. Collisions can be elastic or inelastic.
Fan Cart Physics
Gain an understanding of Newton's Laws by experimenting with a cart (on which up to three fans are placed) on a linear track. The cart has a mass, as does each fan. The fans exert a constant force when switched on, and the direction of the fans can be altered as the position, velocity, and acceleration of the cart are measured.
Ray Tracing (Lenses)
Observe light rays that pass through a convex or concave lens. Manipulate the position of an object and the focal length of the lens and measure the distance and size of the resulting image.
Ray Tracing (Mirrors)
Observe light rays that reflect from a convex or concave mirror. Manipulate the position of an object and the focal length of the mirror and measure the distance and size of the resulting image.
JBHM 8th, GP 2, p. 133-176
Glencoe 7th Grade Mathematics Application and Concepts Course 2, Chapter 4, p. 172-175
Lesson Plan in Word Format (Click Cancel if asked to Log In) Resources:
Professional Texts:
Literary Texts
Mathematics in Children's Literature:
Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annontated Lists of Children's Literature including the math concepts and grade levels. Click on the following link, http://libguides.nl.edu/mathinchildrenslit, then look under Math and Literature Bibliographies.
Connect Four game format: Students play a generalized version of connect four, gaining the chance to place a piece on the board by answering arithmetic questions (addition, subtraction, multiplication, division). Parameters: time, difficulty level, types of questions. Arithmetic Four is one of the Interactivate assessment games.
Related Topics: addition, arithmetic, assessment, division, integers, multiplication,
http://illuminations.nctm.org/LessonDetail.aspx?ID=L733 Students will use vertical movement of an elevator to evaluate signed number expressions. The idea behind the method of adding and subtracting signed integers offerred in this lesson and the next is that the number of rules that students have to memorize and the amount of understanding are minimal, while the underlying concepts are not trivialized
Flipping for Integers
http://illuminations.nctm.org/LessonDetail.aspx?ID=L734 In this lesson, students will adapt expressions that add or subtract two signed integers. This lesson builds on the previous lesson in the unit, where students add/subtract just a positive integer from a signed integer. Then, students will play a game that practices adding and subtracting with signed integers. The game will enforce the skill of arithmetic with integers, but will also get students thinking about maximizing their sum, and ordering signed numbers
Fun with Baseball Stats
http://illuminations.nctm.org/LessonDetail.aspx?ID=L257 The following grades 6-8 activities allow students to explore statistics surrounding baseball. They are exposed to connections between various mathematical concepts and see where this mathematics is used in areas with which they are familiar. This lesson plan is adapted from the May 1996 edition of Mathematics Teaching in the Middle School.
Ideas with Food Unit
http://illuminations.nctm.org/LessonDetail.aspx?ID=U78 The following lessons focus on student organization, preparation, and presentation of some simple foods as a way of applying various mathematical concepts, with problem-solving techniques being central to almost all the activities. This unit was adapted from the "Ideas" column in the February 1994 issue of The Arithmetic Teacher, Vol. 41, No. 6, pp. 309.
Module 1: Preparing To Teach Proportional Reasoning
http://www.teachersdomain.org/resource/scl10.plr.module1/ Clicking on "View" at the left under "Teacher Activity" takes you to Teaching Module 1: Preparing To Teach Proportional Reasoning. This interactive teaching module addresses the necessary knowledge and skills students should master in order to understand the mathematics of proportional reasoning and scaling
Multiplying Integers Using Videotape
http://illuminations.nctm.org/LessonDetail.aspx?ID=L285 In this lesson, students experience beginning-algebra concepts through discussion, exploration, and videotaping. The concept of multiplication of integers is presented in a format which encourages understanding, not simply rote memorization of facts. This lesson plan is adapted from the article, "A Videotaping Project to Explore the Multiplication of Integers", by Marcia B. Cooke, which appeared in Arithmetic Teacher, Vol. 41, No. 3 (November 1993) pp. 170-171
Power Up
http://illuminations.nctm.org/LessonDetail.aspx?ID=L699 Using old batteries and a voltage sensor, students get a real feel of the meaning of negative and positive numbers. Students explore addition of signed numbers by placing batteries end to end (in the same direction or opposite directions) and observe the sum of the batteries’ voltages
Real Estate Tycoon
http://illuminations.nctm.org/LessonDetail.aspx?ID=L279 In this year-long project, students design, "build," and "sell" a house; after which they simulate investment of the profits in the stock market. Along the way, students make scale drawings, compute with fractions and decimals in various contexts, and even solve simple equations. This lesson plan was adapted from an article by David B. Smith, which appeared in the September 2000 edition of Mathematics Teaching in the Middle School.
Too Big or Too Small?
http://illuminations.nctm.org/LessonDetail.aspx?ID=L252 In this lesson, students develop number sense through a series of three hands-on activities. Students explore the following concepts: the magnitude of a million, fractions between 0 and 1, and the effect of decimal operations
Content: Solving Problems with Expressions, Equations, and Inequalities (w/o percentages)
Theme Essential Question:
Essential Questions:
Standards:
Objectives:
Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team
The percentage problems associated with expression, equations, and inequalities have been moved to Unit 3 on Ratios and Proprotions. The problems omitted in this unit will be re-introduced in lesson 3-5.
Background Information
Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials at http://www.azed.gov/educator-certification/
Assessment:
Product
Problem solving using equations
- Students will work with a partner to design a problem that uses a bar model.
- They will solve for an appropimate solution.
- They will find the actual solution and compare the two solutions.
- They will prepare a display of their work.
ORStruggling Students
Key Questions
Observable Student Behaviors
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary:
Inequalities
Inequality signs
Inverse operations
Solution set
Validate
Suggested Activities:
- Houghton Mifflin On Core Mathematics Middle School Grade 7 Unit 3-6, p. 77-80
- ABC Mastering the Common Core in Mathematics Chapter 9.10, p. 111
- Teaching the Common Core Math Standards with Hands-On Activities
- 7.EE.3, Activity, Estimation Game, p. 108
Gizmo- Air Track
Adjust the mass and velocity of two gliders on a frictionless air track.Measure the velocity, momentum, and kinetic energy of each glider as they approach each other and collide. Collisions can be elastic or inelastic.
- Fan Cart Physics
Gain an understanding of Newton's Laws by experimenting with a cart (on which up to three fans are placed) on a linear track. The cart has a mass, as does each fan. The fans exert a constant force when switched on, and the direction of the fans can be altered as the position, velocity, and acceleration of the cart are measured.- Ray Tracing (Lenses)
Observe light rays that pass through a convex or concave lens. Manipulate the position of an object and the focal length of the lens and measure the distance and size of the resulting image.- Ray Tracing (Mirrors)
Observe light rays that reflect from a convex or concave mirror. Manipulate the position of an object and the focal length of the mirror and measure the distance and size of the resulting image.Diverse Learners
Homework: (Teacher Discretion)
Terminology for Teachers:
Ethnicity/Culture | Immigration/Migration | Intercultural Competence | Socialization | Racism/Discrimination
High Yield Strategies
Similarities/Differences | Summarizing/Notetaking | Reinforcing/Recognition | Homework/Practice |
Non-Linguistic representation | Cooperative Learning | Objectives/Feedback |
Generating-Testing Hypothesis | Cues, Questions, Organizers
Resources:
Professional Texts:
Literary Texts
- Mathematics in Children's Literature:
Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annontated Lists of Children's Literature including the math concepts and grade levels.Click on the following link, http://libguides.nl.edu/mathinchildrenslit, then look under Math and Literature Bibliographies.
- Middle & High School: Literature in Mathematics
Many books include websites with lesson ideas.http://sci.tamucc.edu/~eyoung/middle_school_literature.html
- Lesson Plans for Using Literature in Middle and High School Mathematics
(developed by Leonor and edited by Elaine)http://sci.tamucc.edu/~eyoung/Literature%20webpages/Leonor/index.html
- Miscellaneous Math and Children's Literature
http://sci.tamucc.edu/~eyoung/literature.htmlInformational Texts
Art, Music, and Media
Manipulatives
Games
- http://www.mathchimp.com/7thGrade.php
- http://www.sumdog.com/ A variety of games covering many math topics
- http://www.mathplayground.com/SMP_index.html
Connect Four game format:Students play a generalized version of connect four, gaining the chance to place a piece
on the board by answering arithmetic questions (addition, subtraction, multiplication,
division). Parameters: time, difficulty level, types of questions. Arithmetic Four is one of
the Interactivate assessment games.
- Related Topics: addition, arithmetic, assessment, division, integers, multiplication,
negative number, positive number, positive part of the operand, subtraction, wholenumbers
http://www.shodor.org/interactivate/activities/AlgebraFour/
Videos
- Discovery Learning http://www.discoveryeducation.com/
- The Teaching Channel
The teaching Channel currently offers videos of K-12 mathematics teaching aligned withthe Common Core Sate Standards, which would be perfect for professional
development with teacher teams.
https://www.teachingchannel.org/videos?categories=topics common-core
Smartboard Lessons, Promethean Lessons
Other Activities, etc.
- Elevator Arithmetic
http://illuminations.nctm.org/LessonDetail.aspx?ID=L733Students will use vertical movement of an elevator to evaluate signed number expressions.
The idea behind the method of adding and subtracting signed integers offerred in this lesson and the next is that the number of rules that students have to memorize and the amount of understanding are minimal, while the underlying concepts are not trivialized
- Flipping for Integers
http://illuminations.nctm.org/LessonDetail.aspx?ID=L734In this lesson, students will adapt expressions that add or subtract two signed integers. This lesson builds on the previous lesson in the unit, where students add/subtract just a positive integer from a signed integer.
Then, students will play a game that practices adding and subtracting with signed integers. The game will enforce the skill of arithmetic with integers, but will also get students thinking about maximizing their sum, and ordering signed numbers
- Fun with Baseball Stats
http://illuminations.nctm.org/LessonDetail.aspx?ID=L257The following grades 6-8 activities allow students to explore statistics surrounding baseball. They are exposed to connections between various mathematical concepts and see where this mathematics is used in areas with which they are familiar. This lesson plan is adapted from the May 1996 edition of Mathematics Teaching in the Middle School.
- Ideas with Food Unit
http://illuminations.nctm.org/LessonDetail.aspx?ID=U78The following lessons focus on student organization, preparation, and presentation of some simple foods as a way of applying various mathematical concepts, with problem-solving techniques being central to almost all the activities. This unit was adapted from the "Ideas" column in the February 1994 issue of The Arithmetic Teacher, Vol. 41, No. 6, pp. 309.
- Magic Squares
http://illuminations.nctm.org/LessonDetail.aspx?ID=L263This lesson explores magic squares from both a historical and mathematical perspective. The mathematical analysis leads into symbolic algebraic representation of the patterns. This lesson is based upon an article from the April 2001 edition of Mathematics Teaching in the Middle School.
- Module 1: Preparing To Teach Proportional Reasoning
http://www.teachersdomain.org/resource/scl10.plr.module1/Clicking on "View" at the left under "Teacher Activity" takes you to Teaching Module 1: Preparing To Teach Proportional Reasoning. This interactive teaching module addresses the necessary knowledge and skills students should master in order to understand the mathematics of proportional reasoning and scaling
- Multiplying Integers Using Videotape
http://illuminations.nctm.org/LessonDetail.aspx?ID=L285In this lesson, students experience beginning-algebra concepts through discussion, exploration, and videotaping. The concept of multiplication of integers is presented in a format which encourages understanding, not simply rote memorization of facts. This lesson plan is adapted from the article, "A Videotaping Project to Explore the Multiplication of Integers", by Marcia B. Cooke, which appeared in Arithmetic Teacher, Vol. 41, No. 3 (November 1993) pp. 170-171
- Power Up
http://illuminations.nctm.org/LessonDetail.aspx?ID=L699Using old batteries and a voltage sensor, students get a real feel of the meaning of negative and positive numbers. Students explore addition of signed numbers by placing batteries end to end (in the same direction or opposite directions) and observe the sum of the batteries’ voltages
- Real Estate Tycoon
http://illuminations.nctm.org/LessonDetail.aspx?ID=L279In this year-long project, students design, "build," and "sell" a house; after which they simulate investment of the profits in the stock market. Along the way, students make scale drawings, compute with fractions and decimals in various contexts, and even solve simple equations. This lesson plan was adapted from an article by David B. Smith, which appeared in the September 2000 edition of Mathematics Teaching in the Middle School.
- Too Big or Too Small?
http://illuminations.nctm.org/LessonDetail.aspx?ID=L252In this lesson, students develop number sense through a series of three hands-on activities. Students explore the following concepts: the magnitude of a million, fractions between 0 and 1, and the effect of decimal operations
- Volt Meter
http://illuminations.nctm.org/ActivityDetail.aspx?ID=152This applet allows you to learn about positive and negative numbers, by exploring the voltage of batteries.
Language
Arts
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
7 Matrix
Accelerated 7
Matrix
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Home K-2
Home 3-6
Home 6-8
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6